## New technique: Almost Locked Sub-Sets

Advanced methods and approaches for solving Sudoku puzzles

### Re: New technique: Almost Locked Sub-Sets

An example just found on this very forum from the daily puzzle a weak ago:
http://forum.enjoysudoku.com/may-31-2016-t33133.html#p251134
Code: Select all
`+----------+---------------+-------------+| 9 5   12 | 4   28   7    | 168 3   26  || 3 128 4  | 6   2589 289  | 7   125 259 || 7 28  6  | 235 1    2389 | 589 25  4   |+----------+---------------+-------------+| 2 9   3  | 7   6    5    | 4   8   1   || 1 7   8  | 23  4    23   | 56  9   56  || 6 4   5  | 1   89   89   | 2   7   3   |+----------+---------------+-------------+| 5 12  12 | 9   7    6    | 3   4   8   || 8 6   9  | 25  3    4    | 15  125 7   || 4 3   7  | 8   25   1    | 59  6   259 |+----------+---------------+-------------+`

To avoid DP on R26C56 we have {2, 5} an ALSS of R2C56, now:
Edit: Typo in elimination
ALSS-XZ rule: (2=5) R2C56 - (5=2) R9C5 => R1C5 <>2; stte
Last edited by omerosler on Sun Jun 05, 2016 9:48 pm, edited 2 times in total.
omerosler

Posts: 16
Joined: 31 May 2016

### Re: New technique: Almost Locked Sub-Sets

You mean r1c5=8.
I would have done it with the externals (more used to that).
8r1c5=DP=289r236c6You mean r1c5=8.

Sorry, but i cant find a sample here, which would be easier for me with new definitions.

You either have a UR with a a 47 pair in r4c289 or 3r4c2 -> 345r4c125, which locks 4 to r4c12

The Sue de Coq can be found in many ways by manual players, e.g. starting with the 189ALS in r5 or 789ALS in b6:
Either 7r4c7 or 18r5c59-> 479r4c7,r5c78 => r4c8<>7
Looking deeper you can extend the ALS's to find the other Sue de Coq eliminations.
(i never look directly for Sue de Coqs).
Last edited by eleven on Sun Jun 05, 2016 9:48 pm, edited 2 times in total.
eleven

Posts: 2007
Joined: 10 February 2008

### Re: New technique: Almost Locked Sub-Sets

eleven wrote:You mean r1c5=8.
Right, fixed.
I would have done it with the externals (more used to that).
8r1c5=DP=289r236c6-(2=8)r1c5

Sorry, but i cant find a sample here, which would be easier for me with new definitions.
You either have a UR with a 47 pair in r4c289 or 3r4c2 -> 346r4c125, which locks 4 to r4c12

Well, I assume that for many solvers this is nothing new, only new terminology; but I haven't seen this type of elimination as some pattern, only as some kind of forcing chain.
Those subsets (arising from possible DP/AICs like in the nested ALS method/whatever) really behave exactly like ALS so extending ALS elimination rules for them is just an extension to the "mechanical part of solving" - the few steps you do in every puzzle until no more can be done and then you search for the deeper logic of the puzzle (computers narrow the gap from humans via more advanced mechanical methods like forcing nets which humans [usually] can't understand...). Right now this chain method is in the second part (as you [I presume] don't look for this ALSS-XZ elimination the same way you look for ALS-XZ [if at all]) and what I try to do is bring it to the first part, to call puzzles that collapse with this method "unmysterious" and move them from Extreme+ category to an easier category (of puzzles which are mechanichly solvable).

The Sue de Coq can be found in many ways by manual players, e.g. starting with the 189ALS in r5 or 789ALS in b6:
Either 7r4c7 or 18r5c59-> 479r4c7,r5c78 => r4c8<>7
Looking deeper you can extend the ALS's to find the other Sue de Coq eliminations.
(i never look directly for Sue de Coqs).

You're right of course, Sue de Coq can definitely be prooved using ALS-rules with ALSes that shares cells.
It was just a way to show how ALSSes can share cells in their eliminations and the only two examples I could think of are Sue de Coq and David's nested ALS technique (I actually do look for them as they are much easier to spot then ALS-XZ).
omerosler

Posts: 16
Joined: 31 May 2016

### Re: New technique: Almost Locked Sub-Sets

Ok, these are different point of views.
When solving puzzles i try to avoid mechanical searches (like for Sue de Coqs or finned swordfish) as much as possible - but of course i am falling back to some, when i am stuck.
eleven

Posts: 2007
Joined: 10 February 2008

### Re: New technique: Almost Locked Sub-Sets

omerosler wrote:If you think a better name is appropriate, by all means suggest one;
However, it does have a connection to ALS more then how I discovered it:.....

The problems with your ALSS term are
1) It's not distinctive enough and is easily confused with ALSs (the plural of ALS). It might even be a typing error.
2) You are asking players are to 'unlearn' a term they may have struggled to understand and commit to memory and replace it with one that offers no great benefit, in fact rather the reverse because the source of the ALSS has to be identified separately.

To avoid DP on R26C56 we have {2, 5} an ALSS of R2C56, now:
ALSS-XZ rule: (2=5) R2C56 - (5=2) R9C5 => R1C5 <>2; stte

However this existing notation does the job more succinctly
(2)r2c56 =[(89)UR:r26c56]= (5)r2c5 - (5=2)r9c5 => r1c5 <> 2; stte

You may be unfamiliar with the =[Pattern]= notation but it shows the use of a derived inference from a pattern that would be difficult to express using other means – most commonly because the links wouldn't alternate properly.

The inference chains you'll build will be a mix of pattern subsets and simple bilocals and bivalues so, in most players eyes, can't be described as purely composed of subsets. The novelty of your technique is being alert to the possible interactions between subsets from adjacent patterns in the chain. Therefore the best name I can suggest is the 'Interacting Pattern Technique' or IPT.

If you go with that or something similar you can then prefix any chain with 'IPT:' and indicate the source patterns in-line using their familiar forms. But note, in your AIC example there is only one pattern as such!

I don't use nets/forcing chains so you should consider how well this approach would cater for them.

I assure you that I make all these points in a constructive way to help you get an appreciation of the custom and practices that have evolved here. New ideas such as this one of yours and the others you hint you have up your sleeve are always welcome but how well they will be adopted by the majority will depend how well they are presented and how easily they will fit in.

David
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David P Bird
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Location: Middle England

### Re: New technique: Almost Locked Sub-Sets

http://forum.enjoysudoku.com/wxyz-wings-t30012.html

...way back when...

I purposed an als-xz with a subset pattern
{whom ronk and several others} pointed out it could be a case of an als-xy rule but at the same time it was noted that it could be also classed as an Aals - XZ rule
{almost almost locked set} and that i should follow it up with a definition exemplars etc which i never did.
From empirical testing the move was often replicated by an als-xy or a smaller als-xz rule

a side from that: here is the original pattern i discovered and purposed.
Code: Select all
`| .   wxz   .  | . . . | wy   .    . || xz  -xz  -xz | . . . | .   xyz   . || .     .   .  | . . . | .    .    . |`
Some do, some teach, the rest look it up.

StrmCkr

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Joined: 05 September 2006

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